A&A441,513–532(2005) Astronomy DOI:10.1051/0004-6361:20042063 & (cid:1)c ESO2005 Astrophysics The all-sky distribution of 511 keV electron-positron (cid:1) annihilation emission J.Knödlseder1,P.Jean1,V.Lonjou1,G.Weidenspointner1,N.Guessoum2,W.Gillard1,G.Skinner1, P.vonBallmoos1,G.Vedrenne1,J.-P.Roques1,S.Schanne3,B.Teegarden4,V.Schönfelder5,andC.Winkler6 1 Centred’ÉtudeSpatialedesRayonnements,CNRS/UPS,BP4346,31028ToulouseCedex4,France e-mail:[email protected] 2 AmericanUniversityofSharjah,CollegeofArts&Science,PhysicsDepartment,POBox26666,Sharjah,UAE 3 DSM/DAPNIA/SAp,CEASaclay,91191Gif-sur-Yvette,France 4 LaboratoryforHighEnergyAstrophysics,NASA/GoddardSpaceFlightCenter,Greenbelt,MD20771,USA 5 Max-Planck-InstitutfürExtraterrestrischePhysik,Postfach1603,85740Garching,Germany 6 ESA/ESTEC,ScienceOperationsandDataSystemsDivision(SCI-SD),2201AZNoordwijk,TheNetherlands Received24September2004/Accepted20May2005 Abstract.Wepresentamapof511keVelectron-positronannihilationemission,basedondataaccumulatedwiththeSPIspec- trometeraboardESA’sINTEGRALgamma-rayobservatory, thatcoversapproximately∼95%ofthecelestialsphere.Within the exposed sky area, 511 keV line emission is significantly detected towards the galactic bulge region and, at a very low level,fromthegalacticdisk.Thebulgeemissionishighlysymmetricandiscentredonthegalacticcentrewithanextension of∼8◦ (FWHM).Theemissionisequallywelldescribedbymodelsthatrepresent thestellarbulgeorhalopopulations. The detectionsignificance of thebulgeemissionis∼50σ, thatof thegalacticdiskis∼4σ.Thediskmorphology isonlyweakly constrainedbythepresentdata,beingcompatiblewithboththedistributionofyoungandoldstellarpopulations.The511keV linefluxfromthebulgeanddiskcomponentsis(1.05±0.06)×10−3phcm−2s−1and(0.7±0.4)×10−3phcm−2s−1,respectively, correspondingtoabulge-to-diskfluxratiointherange1−3.Assumingapositroniumfractionof f =0.93thistranslatesinto p annihilationratesof(1.5±0.1)×1043 s−1and(0.3±0.2)×1043 s−1,respectively.Theratioofthebulgeluminositytothatof thediskisintherange3−9.Wefindnoevidenceforapoint-likesourceinadditiontothediffuseemission,downtoatypical fluxlimitof∼10−4 phcm−2s−1.Wealsofindno evidence forthepositivelatitudeenhancement that hasbeenreported from OSSEmeasurements;our3σupperfluxlimitforthisfeatureis1.5×10−4phcm−2s−1.Thediskemissioncanbeattributedto theβ+-decayoftheradioactivespecies26Aland44Ti.Thebulgeemissionarisesfromadifferentsourcewhichhasonlyaweak ornodiskcomponent. Wesuggest thatTypeIasupernovae and/or low-massX-raybinariesaretheprimecandidatesforthe sourceofthegalacticbulgepositrons.Lightdarkmatterannihilationcouldalsoexplaintheobserved511keVbulgeemission characteristics. Keywords.gammarays:observations–line:profiles–Galaxy:center 1. Introduction (Rudaz & Stecker 1988; Boehm et al. 2004), and stars ex- pelling radioactive nuclei produced by nucleosynthesis, such Sincethefirstdetection(Johnson&Haymes1973)andthesub- assupernovae(Clayton1973),hypernovae(Casséetal.2004), sequentfirmidentification(Leventhaletal.1978)ofthegalac- novae (Clayton & Hoyle 1974), red giants (Norgaard 1980), tic 511 keV annihilation line, the origin of galactic positrons and Wolf-Rayetstars (Dearborn& Blake 1985). Itseems dif- hasbeenalivelytopicofscientificdebate.Amongtheproposed ficulttodisentangletheprimarygalacticpositronsourcebased candidates for sources of positrons figure cosmic-ray interac- onlyontheoreticalgrounds,mainlyduetothe(highly)uncer- tions with the interstellar medium (Ramaty et al. 1970), pul- tain positron yields, but also due to the uncertain distribution sars (Sturrock 1971), compact objects housing either neutron anddutycycleofthesourcepopulations. stars or black holes (Ramaty & Lingenfelter 1979), gamma- Help is expected from a detailed study of the 511 keV ray bursts (Lingenfelter & Hueter 1984), (light) dark matter line emission morphology. The celestial 511 keV intensity distribution should be tied to the spatial source distribution, (cid:3) Based on observations with INTEGRAL, an ESA project with althoughpositrondiffusionandeffectsassociatedwiththean- instruments and science data centre funded by ESA member states (especially the PI countries: Denmark, France, Germany, Italy, nihilation physics may to some extent blur this link. First es- Switzerland, Spain), Czech Republic and Poland, and with the par- timationsofthe511keVemissionmorphologywereobtained ticipationofRussiaandtheUSA. bytheOrientedScintillationSpectrometerExperiment(OSSE) Article published by EDP Sciences and available at http://www.edpsciences.org/aaor http://dx.doi.org/10.1051/0004-6361:20042063 514 J.Knödlsederetal.:Theall-skydistributionof511keVelectron-positronannihilationemission on-board the Compton Gamma-Ray Observatory (CGRO) 2. Observationsanddatapreparation satellite (Purcell et al. 1994; Cheng et al. 1997; Purcell et al. The data that were analysed in this work consist of those in- 1997; Milne et al. 2000; Milne et al. 2001), but observations cluded in the December 10, 2004 public INTEGRAL data wererestrictedtotheinnerGalaxy,givingonlyalimitedview release (i.e. orbital revolutions 19−76, 79−80, 89−122) plus ofthe511keVemissiondistribution.WiththelaunchofESA’s the INTEGRAL Science Working Team data of the Vela re- INTEGRAL satellite in October 2002, a new gamma-ray ob- gion observed during revolutions 81−88. The data span the servatory is available that allows a detailed study of positron IJD epoch 1073.394−1383.573, where IJD is the Julian Date annihilation signatures. In particular, the imaging spectrome- minus2451544.5days. terSPI(Vedrenneetal.2003),oneofthetwoprimeinstruments We screenedthedata foranomalouslyhighcountingrates on-boardINTEGRAL,hasbeenoptimisedforthestudyofline (typicallyoccurringatthebeginningandtheendofanorbital radiation, combining high-resolution spectroscopy (R ∼ 250 at511keV)withmodestangularresolution(3◦FWHM). revolutiondueto theexitandentryofthe radiationbelts) and for periods of solar activity (as monitored by the SPI antico- Wepresentinthisworkanall-skymapof511keVgamma- incidence system) and excluded these periods from the data. ray lineemission, with thegoalsofdeterminingthemorphol- This data screening has turned out to be crucial for reduc- ogy of the emission in the Galaxyand of searchingforprevi- ing the systematic uncertaintiesin the data analysis related to ously unknownsourcesof511keV emission anywherein the instrumental background variations. After data screening, the sky.Thepresentpublicdataarchivedoesnotyetcovertheen- datasetconsistsof 6821pointedobservations,with a totalex- tire celestial sphere, but the unexposed regions are limited to posure time of 15.3 Ms. Typical exposure times per pointing afewareasathighgalacticlatitudes,comprisinglessthan5% are 1200−3400 s, but a few long staring observations of up ofthesky.Theresultingpoint-sourcesensitivityisbetterthan to113ksexposuretimearealsoincluded. 2×10−4phcm−2s−1formanyregionsalongthegalacticplane, Figure 1 showsa map of the resulting effective SPI expo- allowing for the first time the extractionof informationabout sure at 511 keV. The maximum exposure of 2.1× 108 cm2s thedistributionofpositronannihilationallovertheGalaxy.We occurs towards the galactic centre region thanks to data ob- donotaddressthedistributionofpositroniumcontinuumemis- tained during a long dedicated observation of this region1. A sion in this paper, since the subtraction of the diffuse galac- relativelyuniformexposureof∼3×107cm2shasbeenachieved tic continuum emission is a distinct data analysis challenge. forgalacticlongitudes|l|≤50◦andlatitudes|b|≤15◦.Regions A map of positronium continuum emission will be presented of peculiarly high exposure (∼5 × 107 cm2s) are found in elsewhere(Weidenspointneretal.,inpreparation). Cygnus,VelaandtowardstheLargeMagellanicCloud.Inad- dition,particularlywellexposedsources(>∼2×107 cm2s) are Earlierresultsonthe511keVlineemissionmorphologyas theCrabnebula,3C273,NGC4151,M94,NGC936(during observed by SPI have been presented by Jean et al. (2003a), theSN2003gsoutburst)andtheComacluster.Unexposedre- Knödlseder et al. (2004), and Weidenspointner et al. (2004), gionsarefoundmostlyatintermediategalacticlatitudes(|b| ∼ and were based on observations performed during the galac- 30◦−60◦),andtowardsthesouthgalacticpole. tic centre deep exposure (GCDE) of 2003. Using a “light A mapoftheresultingnarrow-line3σpoint-sourcesensi- bucket” approachwhich neglects the coding propertiesof the tivity of SPI at 511 keV is shown in Fig. 2. To evaluate the SPI mask, Teegarden et al. (2005) derived upper limits on sensitivity, an energy band of 7 keV centred at 511 keV has electron-positronannihilation radiation from the galactic disk been used. The choice of such a relatively wide band elimi- using core-programme data combined with open-programme natesanybiasduetothegermaniumdetectordegradationand observationsatlowgalacticlatitudes(|b|≤20◦).Inthepresent annealingcycles,aswellasanybias/effectduetogaincalibra- paperweprovideforthefirsttimeanall-skyanalysisusingall tionuncertainties.Italsotakesintoaccountmoderate511keV publicdataofthefirstINTEGRALmissionyear. linebroadening,asreportedbyJeanetal.(2003a). Over large regions of the sky, and in particular in the Spectroscopiccharacteristicsofthe511keVlinebasedon galacticplane,asensitivitybetterthan2×10−4 phcm−2s−1 is SPI data have been published by Jean et al. (2003a), Lonjou reached.Abestpoint-sourcesensitivityof5×10−5phcm−2s−1 et al. (2004), and Churazovet al. (2005). We will present the isachievedtowardsthegalacticcentredirection.Thesensitiv- 511 keV line profile that we obtain from the all-sky dataset ity to extended diffuse emission becomes slightly worse with elsewhere(Jeanetal.,inpreparation). increasingemissionsize,anddependsontheexposurepattern intheregionofinterest.Forexample,fora2dangularGaussian This paper is organised as follows. Section 2 describes surface brightness distribution centred on the galactic centre, the observations and the data preparation. Section 3 explains the511keVlinesensitivityworsensfrom5×10−5phcm−2s−1 the treatment of the instrumental background. In Sect. 4, we foragalacticcentrepoint-sourceto7×10−5phcm−2s−1foran presentthefirstall-skymapof511keVgamma-raylineradia- extendedsourceof8◦ FWHM. tionanddeterminethemorphologyoftheemission.Section4 Only single-detector event data have been analysed in also describesearchesforcorrelationswith tracersofgalactic this work (multiple-detector event data do not contribute sig- source populationsin order to shed light on the origin of the nificantly to the SPI sensitivity at an energy of 511 keV; positrons.In Sect. 5 we discussthe implicationsof theobser- vations for the galactic origin of positrons, and we conclude 1 To obtain the effective exposure time, the exposure has to be inSect.6. dividedbytheeffectiveareaat511keVofabout75cm2. J.Knödlsederetal.:Theall-skydistributionof511keVelectron-positronannihilationemission 515 Fig.1. Mapof theeffectiveSPIexposure at 511keV forthedataset analysed inthiswork. Thecontours arelabelledinunitsof107 cm2s, correspondingto13ks(0.1),133ks(1),667ks(5),and1.3Ms(10)ofeffectiveexposuretimes. 1 2 2 5 followingbythepointingnumberp,thedetectornumberdand theenergybine,isthengivenby 5 b =bcont +bline (1) 2 p,d,e p,d,e p,d,e 25 2 5 2 5 2 (note that for the analysis presented in this work a sin- 1 0.5 1 gle energy bin has been used, covering the energy inter- 5 2 1 val 507.5−514.5 keV; however, for clarity and reference in 2 5 1 5 5 future works we give here the complete energy-dependent 5 5 2 2 formalism). 5 2 The time variation of the continuum component is ex- trapolated from that observed in an continuum energy band Fig.2. SPI narrow line 3σ point-source sensitivity at 511 keV for adjacenttothe511keVline.We usedtheenergyband E = theanalysisinterval507.5−514.5keV(contoursarelabelledinunits 523−545keV,situatedabovethe511keVline,inordertoadejx- of10−4phcm−2s−1). cludeanybiasduetopositroniumcontinuumemissionthatap- pearsbelow511keV.Toreducethestatisticaluncertaintythat cf. Roques et al. 2003). Energy calibration was performed arises from the limited counting statistics, we smoothed the orbit-wise, resulting in a relative (orbit-to-orbit) calibration timevariationbylocallyadjustingtherateofsaturatedevents precisionof∼0.01keVandanabsoluteaccuracyof∼0.05keV inthegermaniumdetectors(GEDSAT)totheadjacentcounting (Lonjouetal.2004). rate(GEDSATturnedouttoprovideagoodfirstordertracerof The data have been analysed by sorting the events in a thebackgroundvariationinSPI;cf.Jeanetal.2003b).Thepre- 3-dimensional data-space, spanned by the (calibrated) event dictednumberofcontinuumbackgroundcountsindata-space energy, the detector number, and the SPI pointing number. bin(p,d,e)isthengivenby Anenergybinningof0.5keVhasbeenchosen,wellbelowthe bcont = g ×T instrumentalenergyresolutionof2.12keVat511keV. p,d,e p,d p,d (cid:1) (cid:1) ×(cid:1) ∆e × (cid:1)pp(cid:5)+=∆pp−∆p e(cid:5)∈Eadjnp(cid:5),d,e(cid:5), (2) 3. Backgroundmodelling e(cid:5)∈Eadj∆e(cid:5) pp(cid:5)+=∆pp−∆pgp(cid:5),d×Tp(cid:5),d ThemostcrucialstepinSPI dataanalysisconsistsofthepre- where cisemodellingofthetimevariabilityoftheinstrumentalback- ground. In the region of the 511 keV line, the instrumental – g is the GEDSAT rate for detector d, averaged over p,d backgroundconsists of a nearly flat continuum and a (broad- the time period spanned by pointing p, given in units ened)instrumental511keVlineoriginatingfrompositronan- ofcountss−1; nihilation within the telescope (Teegarden et al. 2004). Since – Tp(cid:5),d isthelifetimefordetectordduringpointing p(cid:5),given the time variation of the continuum component differs from inunitsofseconds; thatofthelinecomponentwemodelthemindependently.The – ∆ is the energy bin size for spectral bin e, given in units e background model for a given data-space bin, indexed in the ofkeV(here∆ =0.5keV);and e 516 J.Knödlsederetal.:Theall-skydistributionof511keVelectron-positronannihilationemission – np(cid:5),d,e(cid:5) is the number of observed counts for pointing p(cid:5), detectord,andenergybine(cid:5),giveninunitsofcounts. Thenumberofpointingsusedforsmoothing,givenby2∆ +1, p isdeterminedforeachpointing panddetectord bysatisfying theconstraint   min p(cid:5)+∆p Tp(cid:5),d ≥Tmin. (3) ∆p≥0 p(cid:5)=p−∆p AnaccumulatedlifetimeofT = 20hhasshowntoprovide min Fig.3.ResidualcountrateasfunctionofpointingnumberfortheDETE an optimum compromise between reducing the statistical un- (top) and ORBIT-DETE (bottom) background models for the energy certainty (due to the limited number of events in the adjacent band507.5−514.5keV.Inadditiontothebackgroundmodelsthebest energy band) and reducing the systematic uncertainty (due to fitting2dGaussiansurfacebrightnessmodel(cf.Sect.4.2.2)hasbeen thefactthattheGEDSATratedoesnotpredictthebackground subtractedfromthedata.Forclarity,thedatahavebeenrebinnedinto to infinite precision). In other words, continuum background groupsof50pointings.Theshadedareaindicatescountratevariations variations shorter than ∼20 h are modelled by the GEDSAT of±0.5%.Forcomparison,themaximum511keVlinesignalampli- ratewhilevariationsonlongertimescalesaremodelledbythe tudecorrespondstoapproximately∼2%oftheobservedcountrate. observedeventrateinthe523−545keVband. The time variation of the line component was modelled foreachdetectord andenergybine separatelyusinga multi- deep exposure (GCDE) of the INTEGRAL core program: a componenttemplateoftheform slow(5◦/day)scanofthegalacticplanefromnegativetowards (cid:9) t positive longitudes combined with rapid (3◦/h) excursions in bline =β(1) +β(2) ×g +β(3) g (t(cid:5))e(t(cid:5)−t)/τdt(cid:5). (4) p,d,e d,e d,e p,d d,e d galacticlatitude.Asresult,thelongitudeprofileofthe511keV t0 lineemissionisencodedincountratevariationsontimescales Thistemplateconsistsofaconstanttermβ(1) plustheGEDSAT ofdayswhilethelatitudeprofileisencodedincountratevaria- d,e rateg scaledbyβ(2) plustheGEDSATrateg (t(cid:5))convolved tionsontimescalesofhours.WithinafewhourstheSPIinstru- p,d d,e d mental backgroundis sufficiently stable to be accurately pre- withanexponentialdecaylaw,scaledbyβ(3) (theconvolution d,e dicted by our model, hence the latitude profile is rather well integralistakenfromthestartoftheINTEGRALmissiont up 0 determined. However, on timescales of days the background todatet).Thecoefficientsβ(di,)eofthetemplateareadjusteddur- variations are more difficult to predict to sufficient accuracy, ingtheanalysisforeachSPIdetectordandenergybineusing potentiallyleadingtosystematictrendsinthedeterminationof amaximumlikelihoodfittingprocedure(again,intheanalysis thelongitudeprofile2. presented in this paper only a single energybin is used). The In order to improve the background model on long constanttermhasbeenintroducedtoprovidefornon-linearities timescales, we studied also a class of models where we ad- between the background variation and the GEDSAT rate. In justthelongtermvariationsduringmodelfitting.Forthispur- fact, it turnsoutthat β(1) are negative.An equallygoodback- d,e pose we adjust the model parameters β(2) not only for all ground predictor is obtained if the GEDSAT rate raised to a d,e SPI detectors but also for time intervals of fixed duration T. powerof∼1.1istaken,butusingaconstantinsteadofapower- Inthisway,systematicuncertaintiesinthebackgroundmodel lawhastheadvantageofhavingthebackgroundvariationtem- on timescales longer than T are removed. Fitting the back- platedecomposedintoalinearcombinationofterms.Thethird groundforeachorbitalrevolution(T ∼ 3days)isadequateto component makes provision for a long term build-up that is reduce systematic trends well below the statistical uncertain- seenintheintensityofthe511keVbackgroundline,andthat ties(cf.bottompanelofFig.3).Thismethodissimilar tothe istentativelyattributedtoproductionoftheisotope65Znwhich methodthatweappliedinourearlierworks(Jeanetal.2003a; hasadecaytimeofτ = 352days.Theprecisevalueofτisin Knödlsederetal.2004;Weidenspointneretal.2004),withthe factweaklyconstrainedbythepresentdata,andalinearslope differencethatwenowalsofitthebackgroundmodelforeach providesan equally goodfit of the instrumental511 keV line of the SPI detectors separately, and that we included in ad- background. dition a constant term and a build-up term in the model (see Although the background model defined by Eqs. (1)–(4), Eq. (4)). Hereafter this second background model is called whichhereafteris calledmodelDETE, predictstheinstrumen- ORBIT-DETE. tal backgroundto good accuracy, significant residuals remain aftersubtractingoffthebackgroundmodelandamodelofthe 2 In a preliminary analysis in which we treated a much smaller sky intensitydistribution fromthe data (cf. Fig. 3). We found dataset, systematic background uncertainties suggested a significant thattheseresidualscanleadtosystematicbiasesinthestudyof elongation of the galactic centre bulge emission along the galac- themorphologyofthe511keVemission,inparticularforthe tic plane. This elongation was artificial and had been produced by determination of the longitude profile of the emission. These background variations that were not fully explained by our model. biasescanbeexplainedbythetelescopepointingstrategythat Removingtheshortperiodofdatawiththestrongestbackgroundvari- has been adopted for a large fraction of the galactic centre ationsremovedalsotheapparentelongationofthebulgeemission. J.Knödlsederetal.:Theall-skydistributionof511keVelectron-positronannihilationemission 517 (cid:1) The introductionof additionalparametersin ORBIT-DETE ek = M R fk+b isthe predictednumberofcountsin data i j=1 ij j i with respect to DETE leads to a substantial loss in sensitiv- space bin i after iteration k (b being the predictednumberof i ity. Thedetectionsignificanceof galacticcentre 511keV line instrumental background counts for bin i), N and M are the emissiondropsfrom∼50σforDETEto∼22σforORBIT-DETE. dimensions of the data and image space, respectively, and λk However,itwasfoundthatthestatisticalaccuracyofthemor- is an acceleration factor that is obtained by constrained max- phologydetermination,whichisdrivenbythecountratecon- imum likelihood fitting (with the constraint that the resulting trast in the data-space rather than the count rate level, is not skyintensitiesremainpositive). degradedbytheintroductionofadditionalparameters,aslong To avoid noise artefacts in the weakly exposed regionsof asT >∼2days.Consequently,usingtheORBIT-DETEmodelfor thesky,weweightedtheimageincrementwithaquantitythat the morphologicalcharacterisation of the 511 keV line emis- is(cid:1)related to the sensitivity of the instrument, given by wj = sionistheoptimumchoicethatkeepsahighstatisticalaccuracy ( N R )1/2.Weverifiedthatintroducingthisweightinghadno i=1 ij whilereducingthesystematicuncertaintiesintheanalysis. impactontheimagereconstructioninthewellexposedregions On the other hand, despite the systematic uncertainties, of the sky. In addition, we smoothed the iterative corrections DETE is accurate enough to allow for a precise determina- onthe righthandside of Eq.(5) usinga 5◦ ×5◦ boxcaraver- tion of 511 keV line flux levels. This is related to the fact age.Inthiswaytheeffectivenumberoffreeparametersinthe thatfluxmeasurementsrequireanaveragedeterminationofthe reconstructionisreducedandimagenoiseisdampedtoanac- countratelevelandarenotsensitivetothecountratecontrast. ceptablelevel.Theapplicationofmoresophisticatedimagere- Apparently,the countrate residuals approximatelyaverage to constructionmethodsinvolvingwaveletbasedmulti-resolution zero(cf.Fig.3). algorithms aiming at a complete suppression of image noise Wethereforeoptedforatwostepapproachwherewefirst (Knödlsederetal.1999a)willbepresentedelsewhere. determinethemorphologyusingORBIT-DETE,andthen,using The resulting all-sky image of the 511 keV line emission the optimum morphologyparameters, determine the 511 keV isshowninFig.4,longitudeandlatitudeprofilesoftheemis- flux using DETE. In this way we recover the good sensitivity sionareshownin Fig.5.We havechosento stopthe iterative of SPI for 511 keV flux measurementsthat was reducedby a procedure after iteration 17 since at this point the recovered factorof∼2bytheusageofORBIT-DETE.Thecomparisonof flux and the fit quality correspond approximately to the val- the flux levels determined using DETE and ORBIT-DETE pro- uesthatweachievebyfittingastrophysicalmodelstothedata vides us with a measure of the systematic uncertainty in the (cf. Sect. 4.2). In this way we make sure that we are not in fluxdetermination,whichingeneralissmallerthanthestatis- theregimeofoverfitting,whichischaracterisedbysubstantial ticaluncertaintyobtainedwithDETE.Weaddthesystematicto imagenoiseandartificialimagestructures.Ontheotherhand, thestatisticaluncertaintyinquadratureandquotetheresultas simulationsshowedthatfaintdiffuseemission,asexpectedfor totalerroronthefluxmeasurement.Incaseswhereuncertain- exampleforagalacticdiskcomponent,wouldnotberecovered tiesinthemorphology(suchasthesizeoftheemissionregion) atthispoint. introducesomeuncertaintyontheflux,wehavealsoaddedthis Figure 4 reveals that the 511 keV sky is dominated by uncertaintytothetotalerrorinquadrature. prominent emission from the bulge region of the Galaxy. Beyondthe galactic bulge,no additional511keV emission is 4. Results seen all over the sky, despite the good exposure in some re- gions(e.g.Cygnus,Vela,LMC,anticentre,northgalacticpole 4.1.Imaging region). The 511 keV emission appears symmetric and cen- Todetermineamodelindependentmapofthe511keVgamma- tred on the galactic centre, with indications for a slight lati- ray line intensity distribution over the sky, we employed the tudeflattening.Thelatitudeflatteningcouldbeeitherduetoan Richardson-Lucy algorithm (Richardson 1972; Lucy 1974). inherentasymmetryofthebulgecomponentorduetothepres- This type of algorithm is widely used for image deconvolu- enceofanunderlyingfaintgalacticdiskcomponent.Indeed,if tion, andhasin particularbeensuccessfully employedforthe theRichardson-Lucyiterationsarecontinued,afaintdisk-like analysisofgamma-raydataofCGRO(Knödlsederetal.1999a; structure emerges(cf. Fig. 6). Yet the image starts to become Milneetal.2000). polluted by noise and we cannot exclude the possibility that We implemented the accelerated version ML-LINB-1 of the apparentdisk emission is artificially created by the expo- Kaufman (1987) of the Richardson-Lucy algorithm for our surepatternthatfollowsthe galacticplane.Thereforewe em- analysis, which iteratively updates the sky intensity distribu- ploymorequantitativemethodsinthenextsectiontoassessthe tion fk → fk+1usingtherelation significanceofthepossiblediskemission. j j  (cid:10) (cid:11)  By fitting Gaussian functions to the longitude and lat- (cid:1) fjk+1 = fjk+λkwjfjk iN=1(cid:1)iNen=kii1−Ri1j Rij (5) dietxiuctdeaentetsp,orhfoofithwleeesveemor,fisthstihaotenthitmeoea∼mg1ei3s◦s(ico×fn.1pF0r◦iogfi(.Fle5Ws)HarwMeen).oeFtsiwtgimeulraletree5ptirhnee-- sentedbyGaussianfunctions.Theemissionisbetterdescribed where R is the instrumental response matrix (linking the by a compact (FWHM∼5◦) core and a more extended halo ij data space, indexed by i, to the image space, indexed by j), (FWHM 10◦−20◦). We want to emphasise, however, that this n is the number of counts measured in data space bin i, qualitativeanalysisshould notbe pushedtoo far, since image i 518 J.Knödlsederetal.:Theall-skydistributionof511keVelectron-positronannihilationemission Fig.4. Richardson-Lucy image of 511 keV gamma-ray line emission (iteration 17). Contour levels indicate intensity levels of 10−2, 10−3, and10−4phcm−2s−1sr−1(fromthecentreoutwards). Fig.5.LongitudeandlatitudeprofilesoftheimageshowninFig.4(integrationrange|l|≤30◦,|b|≤30◦). Fig.6.Richardson-Lucyimageafteriteration25.ContourlevelsaresimilartoFig.4. J.Knödlsederetal.:Theall-skydistributionof511keVelectron-positronannihilationemission 519 deconvolutionis a non-linearprocess which is easily affected Table1.Morphologyoftheemissionassuminga2dangularGaussian byimagenoiseandexposurebiases. surfacebrightnessdistribution. Quantity Measuredvalue 4.2.Morphologicalcharacterisation RMLR(DOF) 462.2(5) 4.2.1. Method l −0.6◦±0.3◦ 0 To make a quantitative assessment of the morphology of the b0 +0.1◦±0.3◦ 511 keV line emission we use a maximum likelihood multi- ∆l(FWHM) 8.1◦±0.9◦ component model fitting algorithm. Assuming Poisson noise ∆b(FWHM) 7.2◦±0.9◦ for the measured number ni of events in each of the N data- 511keVflux(10−3phcm−2s−1) 1.09±0.04 spacebins,thealgorithmmaximisestheloglikelihood (cid:5)N lnL= n lne −e −lnn!, (6) i i i i i=1 emission appears slightly offset from the galactic centre (cid:1) wheree = α sk +b(β)isthepredictednumberof(source direction, at the statistical 2σ level, but we do not claim that plusbacikgroukndk)ciountisindataspacebini, sk =(cid:1)M fkR is thisoffsetis significant.Fromourearlieranalyseswe learned i j=1 j ij that the centroid can be shifted by this amount simply from the sky intensity model fk folded into the data space (R be- ingtheinstrumentalrespojnsematrix),b(β)isthebackgriojund the combined effect of statistical and systematic biases in the i model(cf.Fig.1),andα andβarescalingfactorsforthesky modellingoftheinstrumentalbackground. k intensity and the background model, respectively, that are Within the statistical uncertainties, the emission appears adjustedbythefit. fullysymmetric,withanextensionof∼8◦(FWHM).Formally, Detection significances (and parameter errors) are esti- wedetermineamarginalemissionflatteningof∆b/∆l=0.89± mated using the maximum likelihood ratio test (Cash 1979). 0.14.Thetotal511keVfluxis(1.09±0.04)×10−3phcm−2s−1, We calculate the maximum log likelihood-ratio MLR = wherethequotederrorincludestheuncertaintyintheextentof −2(lnL −lnL )betweentwomodels(hypotheses),wherefor theemissionandthestatisticalandsystematicmeasurementer- 0 1 thefirstoneweconstrainanumber poftheparameterstospe- rors(cf.Sect.2). cific values (resulting in L ) while for the second one all pa- The RMLR of 462.2 that has been obtained using the 0 rametersareleftfree(resultingin L ).InthecasethatL pro- ORBIT-DETEbackgroundmodelconvertsintoa formaldetec- 1 1 videsasatisfactoryfitofthedata,MLRisthendistributedlike tion significance of 22σ. Using the DETE background model aχ2 distributionwithpdegreesoffreedom.Statisticalparame- andincludingthesystematicuncertaintiesresultsinasubstan- p tererrorswereestimatedusingtheformalismofStrong(1985). tiallyhigherdetectionsignificanceof34σ.Neglectingsystem- Throughoutthispapertheerrorbarsquotedare1σ. atic uncertainties would even boost the detection significance We call the maximum log likelihood-ratio (MLR) of a towards49σ. model the difference between the log likelihood obtained by fittingallmodelparametersandtheloglikelihoodobtainedby fittingonlythebackgroundmodeltothedata(i.e.forL allpa- 4.2.3. Galacticmodels 1 rametersα andβvaryfreelywhileforL allα areconstrained k 0 k To determine the galactic positron-electron annihilation rate tozeroandonlytheβareallowedtovary).Tocomparemod- requires modelling the spatial distribution of the positron- elswithdifferentnumbersoffreeparameters,wequotethere- electron annihilation. The 511 keV photon luminosity L ducedmaximumloglikelihood-ratio,RMLR = MLR−DOF, 511 is related to the positron luminosity L through L = with DOF being the number of free parametersα of the sky p 511 k (2−1.5f )× L where f is the positronium (Ps) fraction, de- intensitymodel. p p p fined as the fraction of positrons that decay via positronium formation(Brown,&Leventhal1987).Using f =0.93±0.04 p 4.2.2. 2dsurfacebrightnessdistribution that has been determined from OSSE observations (Kinzer etal.2001)resultsinaconversionfrom511keVphotonlumi- Asafirststepwecharacterisetheapparentmorphologyofthe nosityto a positron-electronannihilationrate of L = (1.64± 511keVlineemissionontheskyusinga2dangularGaussian p 0.06)×L . surface brightness distribution for which we determined the 511 centroid,l ,b ,thelongitudeandlatitudeextent,∆l,∆b,andthe We herecomparemodelsof bulge,disk,andhalo compo- 0 0 nentswiththe data.Based ongalacticmodeldensitydistribu- 511keVlineflux.Theresultsofthisanalysisaresummarised tions ρ(x,y,z) we calculate the expected all-sky 511 keV in- inTable1,thebestfittingmodelintensitydistributionisshown tensity f(l,b)towardsdirection(l,b)byintegratingthevolume inFig.8. emissivityρ(x,y,z)alongthelineofsights: The analysis confirms our earlier findings (Jean et al. 2003a; Knödlseder et al. 2004; Weidenspointner (cid:9) etal.2004)ofacompactandsymmetric511keVlineemission 1 f(l,b)= ρ(x,y,z)ds (7) distribution towards the galactic centre. The centroid of the 4π 520 J.Knödlsederetal.:Theall-skydistributionof511keVelectron-positronannihilationemission Table2.Galaxymodelfittingresults(seetext).Thecolumnsgive(1)themodel,(2)theRMLR(obtainedusingtheORBIT-DETEbackground model) andthenumber offreemodel parameters(DOF),(3)thebulgescalelength,(4)thebulgescaleheight,(5)−(8)the511keV photon luminosityofthemodelcomponents,and(9)−(12)thetotal4πintegrated511keVlineall-skyfluxineachofthemodelcomponents.Theprime indicates model components for which the scaling parameters were adjusted by the fit.Thefigures in parenthesis quoted inCols. (5)−(12) indicate1σuncertaintiesinthelastdigit. Model RMLR R z L (1043phs−1) 511keVlineflux(10−3phcm−2s−1) 0 0 511 (DOF) (kpc) (kpc) bulge disk halo total bulge disk halo total G0 447.5(1) 0.91 0.51 1.04(3) 1.04(3) 1.22(4) 1.22(4) G1 445.7(1) 0.97(3) 0.97(3) 1.19(4) 1.19(4) G2 450.8(1) 0.98(3) 0.98(3) 1.18(3) 1.18(3) G3 462.2(1) 0.98(3) 0.98(3) 1.18(3) 1.18(3) E1 441.8(1) 0.99(4) 0.99(4) 1.19(4) 1.19(4) E2 453.1(1) 1.01(3) 1.01(3) 1.19(3) 1.19(3) E3 464.9(1) 1.00(3) 1.00(3) 1.17(3) 1.17(3) S 459.0(1) 0.96(3) 0.96(3) 1.19(3) 1.19(3) F E 459.0(1) 0.93(2) 0.93(2) 1.19(3) 1.19(3) F P 456.5(1) 0.94(3) 0.94(3) 1.16(3) 1.16(3) F S 456.3(1) 0.94(2) 0.94(2) 1.22(3) 1.22(3) PR G0’ 462.5(3) 0.52(6) 0.45(5) 0.94(4) 0.94(4) 1.09(4) 1.09(4) E0’ 464.2(3) 0.37(5) 0.42(7) 0.98(5) 0.98(5) 1.15(5) 1.15(5) H’ 468.4(4) 1.6(3) 1.6(3) 2.2(4) 2.2(4) Shells 469.0(2) 0.97(3) 0.97(3) 1.13(3) 1.13(3) E3+D0 466.3(2) 0.95(3) 0.11(5) 1.05(4) 1.11(4) 0.4(2) 1.53(5) G0’+D0 465.2(4) 0.48(6) 0.46(6) 0.87(4) 0.15(5) 1.03(5) 1.01(5) 0.6(2) 1.61(7) E0’+D0 466.2(4) 0.34(4) 0.44(8) 0.92(5) 0.14(5) 1.06(5) 1.07(6) 0.5(2) 1.61(8) H’+D0 468.2(5) 0.09(8) 1.2(3) 1.3(3) 0.4(3) 1.6(5) 2.1(5) Shells+D0 472.2(3) 0.91(4) 0.15(5) 1.05(4) 1.05(4) 0.6(2) 1.62(6) E3+D1 468.8(2) 0.93(4) 0.23(8) 1.15(6) 1.09(5) 0.8(3) 1.90(9) G0’+D1 468.6(4) 0.47(6) 0.45(6) 0.84(5) 0.31(9) 1.15(6) 0.98(5) 1.1(3) 2.1(1) E0’+D1 469.5(4) 0.33(4) 0.42(8) 0.89(5) 0.29(9) 1.17(7) 1.03(6) 1.0(3) 2.1(1) H’+D1 470.4(5) 0.3(1) 1.2(3) 1.4(3) 0.9(4) 1.5(4) 2.4(5) Shells+D1 474.9(3) 0.88(4) 0.29(8) 1.17(6) 1.03(5) 1.0(3) 2.0(1) (the galactic centre has been assumed to be at a distance of modelshavetriaxialmorphologiesthatdifferintheorientation R(cid:9) = 8.5kpc).Galactic511keVphotonluminositiesare cal- angles,thescalelengths,andtheradialdensityprofiles.Details culatedbyintegratingρ(x,y,z)overthegalacticvolume, ofthemodelsaregiveninAppendixA,theresultsoftheanaly- (cid:9) sisaresummarisedinTable2,andbestfitting511keVintensity Lp = ρ(x,y,z)s2dsdΩ (8) distributionsareshowninFig.8. assuminganouterGalaxyradiusofR =15kpc. The best fitting bulge models are E3, G3, SF, and EF. max Reasonably good fits are also obtained for P and S , while Since the 511 keV line emission is primarilyarising from F PR only moderate fits are achieved for the remaining models. the galactic centre region we fitted in a first step models of Ourrankingis similarto thatestablishedfromthe analysisof thegalacticstellarbulgetothedata.Toaccountforuncertain- the DIRBE and DENISnear-infrareddata (Dwek et al. 1995; tiesinourknowledgeaboutthemorphologyofthiscomponent Freudenreich 1998; Picaud & Robin 2004). The best fitting (whicharerelatedtoourlocationinthegalacticplaneamidthe bulge models fit the data as well as the adjusted 2d angular obscurationbyinterstellardust)wecomparedavarietyofpro- Gaussiansurfacebrightnessdistribution.Thismeansthatmod- posedbulgemodelstothedata.Themodelsweregatheredfrom elsofthegalacticstellarbulgeareabletoexplainsatisfactorily Dweketal.(1995)andFreudenreich(1998),whomodelledthe themorphologyofthe511keVbulgeemission. distributionofKandMgiantstarsusingDIRBEnear-infrared skymaps,andfromPicaud&Robin(2004)whoanalyseddata Inasecondstepwefittedthe511keVemissionusingpara- fromtheDENISnear-infraredsurvey.Thereisanaccumulating metric models of the galactic bulge and halo morphology in bodyofevidencethatthestellardistributioninthebulgeisbar- order to determine the scale of the emission. For the bulge shaped,andexceptformodelsG0andE0,allemployedbulge modelsG0’andE0’weadjusttheradialscalelength(R )and 0 J.Knödlsederetal.:Theall-skydistributionof511keVelectron-positronannihilationemission 521 Table3.Summaryof model fittingresults.Fluxesaregivenastotal 4πintegratedall-skyvalues.Annihilationrateshavebeencalculated assuming f =0.93. p Quantity Bulge Halo Disk Flux(10−3phcm−2s−1) 1.05±0.06 1.6±0.5 0.7±0.4 L (1043phs−1) 0.90±0.06 1.2±0.3 0.2±0.1 511 L (1043s−1) 1.50±0.10 2.0±0.5 0.3±0.2 p Totalflux(10−3phcm−2s−1) 1.5−2.9 TotalL (1043phs−1) 1.0−1.7 511 TotalL (1043s−1) 1.6−2.8 p B/Dfluxratio 1−3 B/Dluminosityratio 3−9 outer 0.5−1.5 kpc shell, confirmingthe existence of a narrow core plus an extended halo of 511 keV emission that has al- readybeensuggestedbytheimaginganalysis(cf.Sect.4.1). Fig.7. Radial dependence of the 511 keV volume emissivity as de- In a third step we added galactic disk components to the rivedfromthebulgemodel“Shells”. bulgeandhalomodels.Forthegalacticdiskwetestedmodels of young (model D0) and old (model D1) stellar populations (Robin et al. 2003). With both modelswe find clear evidence verticalscaleheight(z ),whileforthegalactichalomodelH’ 0 for511keVlineemissionfromthegalacticdisk.Addingdisk we determine the density slope powerlaw index (n), the in- models D0 and D1 to bulge or halo models consistently im- ner cutoff radius (a ), and the axis ratio ((cid:10)). In addition, we c provesthefitleadingtoadetectionofthediskemissionatthe employeda modelcomposedofa setof galactocentricnested 3−4σlevel3.Formally,D1providesabetterfitthanD0,butthe shellsofconstantdensity(model“Shells”)todeterminethera- differenceismarginal.Thesignalfromthediskisstilltoofaint dialdensityprofileofthe511keVemission.Wevariedtheradii inourpresentdatasettodeduceanythingaboutitsmorphology. oftheshellsandthenumberofshellsinordertomaximisethe Theflux,luminosityandannihilationrateinthebulge,halo MLR,whilstlimitingthenumberofshellstotheminimumre- and disk components are summarised in Table 3. Recall that quiredtosatisfactorilydescribethedata. the bulgeandhalo componentsare alternativesandtheir con- Thedatasuggestasymmetricbulgeemissionprofile,with tributionshouldnotbeaddedtoderivethetotalgalacticvalues. scalelengthsbetween300and600pc.TheRMLRsarecompa- Either component provides an almost equally good fit to the rabletothebestfittingbulgemodelsthatwetestedbefore.The data.Duetotheirdegeneracyfittingbothsimultaneouslyisnot dataareequallywellfittedbyamodelofthegalactichalo,with meaningful. adensitypowerlawindexofn=3.0±0.3,aninnercutoffradius of a = 0.39±0.08kpc, and a flattening of (cid:10) = 0.81±0.12. The halo model leads to a considerably larger flux, lu- c minosity and annihilation rate than the bulge model due to Most studies of the stellar halo population suggest power in- the presence of a flat and extended tail in this distribution dicesbetween2.4and3.5andflatteningsintherange0.6to1.0, whiletheinnercutoffradiusisbasicallyundetermined(Robin (cf.Fig.8).Currently,ourdatadonotallowtodetectthistail, andthus,theydonotallowtodiscriminatebetweenbulgeand etal.2000,andreferencestherein).Ourvaluesarecompatible halomodels.Futuredeepobservationsatintermediategalactic with those of the stellar halo population, but the large uncer- latitudesthatarescheduledfortheINTEGRALAO-3observ- tainties in the stellar halo morphologydo notallow firm con- ing period aim in measuring this emission tail, promising to clusionstobedrawn. provideconstraintsthatwillallowinthe futuretodisentangle The nested shell model provides the best fit to the data betweenthedifferentemissionmorphologies. thankstoitsflexibilityinadjustingtheradialdensityprofileof The data suggest bulge-to-disk 511 keV flux ratios in the theemission.Asatisfactoryfitisachievedbyusingtwoshells withradii0−0.5and0.5−1.5kpc;splittinguptheseshellsina range1−3,wherethelowerboundaryisobtainedfortheshort scale-length old stellar disk model D1 which suggests larger finerbinning,movingtheshellinterfaceradiusoraddingmore disk flux values than the young stellar disk model D0. Halo- shells does not significantly improve the fit. In particular, we to-disk 511 keV flux ratios are even larger, in the range 2−4, detectnosignificant511keVbulgeemissionfromgalactocen- tricdistances>∼1.5kpc.Theradialdependenceofthe511keV 3 Using the quoted RMLRs, the formal significance of the disk volumeemissivityisplottedinFig.7.Forillustrationweadded emissionamountsonlyto2−3σ.However,thetabulatedRMLRshave the result of a third shell to the figure that covers radial dis- beenobtainedusingtheORBIT-DETEbackgroundmodelwhichisless tancesof1.5−3.0kpcandforwhichthefluxisconsistentwith sensitive to 511 keV line emission than the DETE model. Using the zero. Our fit reveals a drop in the annihilation emissivity by procedureoutlinedinSect.3wereducethefluxuncertaintiesandin- one order of magnitude between the inner 0−0.5 kpc and the creasethedetectionsignificanceto3−4σ. 522 J.Knödlsederetal.:Theall-skydistributionof511keVelectron-positronannihilationemission Fig.8.All-skymapsofthebestfittingmodelsof511keVgamma-raylineemission(seetextforadescriptionofthemodels).Contourlevels indicateintensitylevels(fromthecentreoutwards)of10−2,10−3,and10−4phcm−2s−1sr−1.TheresultingRMLRsofthemodelfitsarequoted intheupper-rightcornerofthepanels. owingtothelargerfluxinthehalocomponent.Thelargeuncer- Inotherwords,toproducethesame511keVfluxatEarth,the taintyintheseratiosarisesfromthelowintensityofthegalac- intrinsicluminosityofthebulgehastobelargerthanthatofthe ticdiskcomponent,whichfortheanalyseddatasetisjustabove disk4. Itisthereforeimportantto quoteexplicitlythequantity theSPIdetectionlimit. forwhichwediscussthebulge-to-diskratio.Thesamerational also holds for the halo-to-disk 511 keV photon luminosity We also note that the bulge-to-disk 511 keV photon lu- minosity ratio is much higher than the bulge-to-disk flux ratio and lies in the range 3−9. This difference is ex- 4 Thedifferencebetweenbulge-to-diskfluxandluminosityratiois p(cid:12)lained by the(cid:12)fact that the average squared distance s¯2 = onlyimportantforourhomeGalaxyandisrelatedtothefactthatthe ρ(s)s2dsdΩ/ ρ(s)dsdΩ,whichdefinesthedistanceatwhich Sun is located within the galactic radius. For external galaxies this asourceofluminosityLp producestheobserved511keVline difference disappears since their bulge and disk appear at the same flux,issmallerforthegalacticdiskthanforthegalacticbulge. distancetous.